#### Published in

Elsevier, Journal of Mathematical Analysis and Applications, 2(361), p. 533-542

## Asymptotic behaviour for small mass in the two-dimensional parabolic–elliptic Keller–Segel model

Journal article published in 2010 by Adrien Blanchet
This paper is made freely available by the publisher.

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#### Abstract

The Keller-Segel system describes the collective motion of cells that are attracted by a chemical substance and are able to emit it. In its simplest form, it is a conservative drift-diffusion equation for the cell density coupled to an elliptic equation for the chemo-attractant concentration. This paper deals with the rate of convergence towards a unique stationary state in self-similar variables, which describes the intermediate asymptotics of the solutions in the original variables. Although it is known that solutions globally exist for any mass less $8π\,$, a smaller mass condition is needed in our approach for proving an exponential rate of convergence in self-similar~variables.